📚 Year 7 OCR Maths: Winter Holiday Intensive Revision Plan | 七年级 OCR 数学：寒假强化复习计划
Getting the most out of the winter break means balancing rest with a structured touch-up of the topics you have covered in Year 7 so far. This article provides a topic‑by‑topic revision guide, complete with key ideas, common mistakes and quick‑fire practice suggestions, all aligned with the OCR KS3 syllabus.
充分利用寒假，既要休息好，也需要有结构地巩固七年级学过的内容。本文提供按主题划分的复习指南，涵盖核心概念、常见错误和随堂练习建议，完全契合 OCR KS3 教学大纲。
1. Setting Goals and Planning | 设定目标与规划
Before you open any notes, spend twenty minutes listing the topics that felt tricky during the autumn term. Write down two or three concrete goals, such as 'I can add fractions with different denominators without help' or 'I can solve two‑step equations confidently'. Then build a weekly timetable that allocates 30–45 minutes a day for maths, mixing topics so you do not get bored.
在翻开笔记之前，先花二十分钟列出秋季学期让你感到吃力的主题。写下两三个具体目标，例如“我能独立进行异分母分数的加法”或“我能自信地解两步方程”。然后制作一份每周时间表，每天安排 30–45 分钟的数学复习，混合不同主题，避免枯燥。
- English: Stick to a routine – same time each day creates a habit. Use a checklist to tick off completed sessions.
- 中文: 坚持固定的日常作息——每天同一时间学习有利于养成习惯。准备一份清单，完成一项就打勾。
- English: Identify your weakest three sub‑topics and tackle them first while your energy is high.
- 中文: 先找出你最薄弱的三个子专题，趁精力最旺盛时优先攻克。
2. Number and Place Value | 数字与位值
Secure place value up to ten millions and down to three decimal places. Practise reading and writing large numbers in words and figures. Make sure you can round whole numbers to the nearest 10, 100, 1000 and decimals to one, two or three decimal places. Estimation is your best friend here.
夯实从千万到小數點后三位的位值概念。练习用文字和数字读写大数。确保你能将整数四舍五入到最接近的 10、100、1000，以及将小数舍入到一、二或三位小数。估算是这里的得力助手。
- English: Write the number 4 307 256 in words. Round it to the nearest thousand.
- 中文: 将数字 4 307 256 写成英文单词 (four million, three hundred and seven thousand, two hundred and fifty‑six)。将它四舍五入到千位。
- English: Round 0.0678 to two decimal places. Check understanding of the digit after the cut‑off point.
- 中文: 将 0.0678 保留两位小数。关注截断位后面的数字如何决定舍入。
3. Four Operations and Negative Numbers | 四则运算与负数
plication. Division can be checked by inverse multiplication. When negatives arrive, a number line helps: –7 + 3 = –4, –5 – 2 = –7. Remember that subtracting a negative is the same as adding the positive.
列竖式加法与减法必须又快又准。12 × 12 以内的乘法口诀必须秒答；并用它们进行短乘与长乘。除法可以用乘法逆运算来检查。遇到负数时，数轴很有帮助：–7 + 3 = –4，–5 – 2 = –7。记住减一个负数等于加它的正数。
- English: Calculate 2357 – 1894 using a column method, then estimate to check.
- 中文: 用竖式计算 2357 – 1894，再估算验证。
- English: Simplify (–4) × 6 and 15 ÷ (–3). What is (–3)²? Caution: (–3)² = 9, not –9.
- 中文: 化简 (–4) × 6 和 15 ÷ (–3)。(–3)² 是多少？注意 (–3)² = 9，不是 –9。
4. Fractions, Decimals and Percentages | 分数、小数与百分比
Know that ½, 0.5 and 50% are equivalent. Practise converting between the three forms. For adding and subtracting fractions, find a common denominator. Multiplying fractions is straightforward: multiply numerators, multiply denominators. To divide, flip the second fraction and multiply. For percentages, find 10% first and scale up or down.
清楚 ½、0.5 和 50% 是等价的。练习三者之间的转换。进行分数加减时，先找公分母。分数乘法很简单：分子相乘、分母相乘。除法则是把第二个分数倒数再相乘。处理百分比时，先找出 10%，再以此为基础缩放。
- English: Convert ⅗ to a decimal and a percentage. Add ⅔ + ¼.
- 中文: 将 ⅗ 转换成小数和百分比。计算 ⅔ + ¼（答案：¹¹⁄₁₂）。
- English: Calculate 40% of 85 kg. Find 15% of £240 using the 10% + 5% method.
- 中文: 求 85 kg 的 40%。用“10% + 5%”法求 £240 的 15%。
5. Basic Algebra | 代数基础
Algebra uses letters to represent numbers. Learn to write expressions like '3 more than n' → n + 3, or 'double a number subtract 5' → 2x – 5. Collect like terms: 4a + 3b – 2b = 3a + 5b. Understand the difference between 2n and n²: 2n means 2 × n, n² means n × n.
代数中用字母代表数。学会写出表达式，如“比 n 多 3” → n + 3，或“一个数的两倍减 5” → 2x – 5。合并同类项：4a + 3b – a + 2b = 3a + 5b。理解 2n 和 n² 的区别：2n 表示 2 × n，n² 表示 n × n。
- English: Simplify 5y + 3 – 2y + 7. If x = 4, find the value of 3x – 2.
- 中文: 化简 5y + 3 – 2y + 7。若 x = 4，求 3x – 2 的值。
- English: Expand brackets: 3(2a + 5) = 6a + 15. Factorise: 8m – 12 = 4(2m – 3).
- 中文: 去括号展开：3(2a + 5) = 6a + 15。因式分解：8m – 12 = 4(2m – 3)。
6. Equations and Sequences | 方程与序列
operations: for x + 5 = 12, subtract 5 from both sides; for 3y = 18, divide by 3. With two‑p equations like 2p + 3 = 11, first subtract 3, then divide by 2. Sequences: spot the term‑to‑ add 3) and use it to find the next terms. Begin to find the nth term for linear sequences.
解方程就是找出使等式成立的数值。使用逆运算：如 x + 5 = 12，两边同减 5；3y = 18，两边同除以 3。对于两步方程如 2p + 3 = 11，先减 3，再除以 2。序列：找出项与项之间的法则（如每次加 3），并用来找出后续项。开始学习寻找线性序列的第 n 项。
- English: Solve 4n – 7 = 9. Write the first five terms of the sequence with nth term 2n + 1.
- 中文: 解方程 4n – 7 = 9。写出第 n 项为 2n + 1 的数列的前 5 项。
- English: Describe the rule for 5, 8, 11, 14… and find the 10th term without listing all terms.
- 中文: 描述数列 5, 8, 11, 14… 的变化规律，并直接求出第 10 项。
7. Measurement and Units | 测量与单位
l = 1000 ml. Time: 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day. Imperial‑metric links such as 1 inch ≈ 2.5 cm may also appear.
公制单位：长度（毫米 mm、厘米 cm、米 m、千米 km），质量（克 g、千克 kg），容量（毫升 ml、升 l）。牢记关键换算：1 cm = 10 mm，1 m = 100 cm，1 km = 1000 m；1 kg = 1000 g；1 l = 1000 ml。时间：60 秒 = 1 分钟，60 分钟 = 1 小时，24 小时 = 1 天。可能出现 1 英寸 ≈ 2.5 cm 等英制与公制的联系。
- English: Convert 3.6 km into metres. How many 250 ml cups can be filled from a 2‑litre bottle?
- 中文: 将 3.6 km 转换为米。一瓶 2 升的饮料可以倒满多少个 250 ml 的杯子？
- English: A film starts at 14:35 and runs for 1 hour 50 minutes. At what time does it end?
- 中文: 一部电影 14:35 开始，片长 1 小时 50 分钟，请问几点结束？
8. Geometry and Angles | 几何与角度
Angles: acute (< 90°), right (90°), obtuse (between 90° and 180°), straight (180°) and reflex (> 180°). Angles on a straight line sum to 180°, around a point 360°, and in a triangle 180°. Use a protractor confidently; estimate first to avoid silly mistakes. Vertically opposite angles are equal.
角：锐角（< 90°），直角（90°），钝角（90° 到 180° 之间），平角（180°），优角（> 180°）。直线上的角之和为 180°，绕一点一周为 360°，三角形内角和为 180°。自信地使用量角器；先估算再测量以避免低级错误。对顶角相等。
- English: If one angle in a triangle is 47° and another is 68°, find the third angle. Draw the triangle roughly.
- 中文: 若三角形一个角为 47°，另一个角为 68°，求第三个角。并粗略画出这个三角形。
- English: Two angles on a straight line are x and 2x. Form an equation and solve for x.
- 中文: 直线上的两个角分别是 x 和 2x。列出方程并解出 x（答案：x = 60°）。
9. Perimeter, Area and Volume | 周长、面积与体积
to use the perpendicular height. Volume of a cuboid = length × width × height, measured in cubes (cm³, m³). Surface area is the total area of all faces.
周长是围绕图形一周的长度。长方形的周长 P = 2(长 + 宽)。长方形面积 = 长 × 宽；三角形面积 = ½ × 底 × 高。注意必须使用垂直高度。长方体体积 = 长 × 宽 × 高，单位为立方单位（cm³, m³）。表面积是所有面的面积之和。
- English: A rectangle is 7 cm by 4 cm. Find its perimeter and area. A triangle shares the same base and height of 4 cm and 5 cm; calculate its area.
- 中文: 一个长方形长 7 cm，宽 4 cm。求它的周长和面积。一个三角形底 4 cm、高 5 cm，求面积。
- English: A cuboid measures 5 cm × 3 cm × 2 cm. Work out its volume and surface area.
- 中文: 一个长方体尺寸为 5 cm × 3 cm × 2 cm。计算它的体积和表面积。
10. Coordinates and Graphs | 坐标与图像
Coordinates are written as (x, y) with the x‑axis horizontal and y‑axis vertical. You need to be comfortable in all four quadrants, where x and y can be negative. Plot points accurately and connect them to form shapes or line graphs. Midpoint of a line segment can be found by averaging the x‑coordinates and y‑coordinates.
坐标写作 (x, y)，其中 x 轴水平，y 轴垂直。你需要熟练掌握所有四个象限，即 x 和 y 都可以是负数。精确描点并将它们连成图形或直线图。线段的中点可以通过取 x 坐标和 y 坐标的平均值来求出。
- English: Plot the points (2, 3), (–1, 3), (–1, –2) and (2, –2). What shape is formed? Find its area.
- 中文: 描出点 (2, 3), (–1, 3), (–1, –2) 和 (2, –2)。组成了什么图形？求它的面积。
- English: What is the midpoint of the line joining (–3, 5) and (7, 1)?
- 中文: 连接 (–3, 5) 和 (7, 1) 的线段的中点坐标是什么？
11. Statistics and Averages | 统计与平均数
You will see bar charts, pictograms, line graphs and possibly pie charts. Always read the scale carefully – does one picture represent 1, 2, 5 or 10? Averages: mode (most frequent), median (middle value when ordered), mean (sum divided by how many) and range (largest minus smallest). It is essential to check whether the data is discrete or continuous.
你可能会遇到条形图、象形图、折线图甚至是饼图。务必仔细阅读刻度——一个图形代表的是 1、2、5 还是 10？平均数：众数（出现最频繁的值），中位数（排序后中间的值），平均数（总和除以个数），以及极差（最大值减最小值）。必须分清数据是离散的还是连续的。
- English: The number of books read by seven pupils: 3, 5, 2, 5, 8, 5, 4. Find the mode, median, mean and range.
- 中文: 七名学生阅读书籍的数量：3, 5, 2, 5, 8, 5, 4。求众数、中位数、平均数和极差。
- English: Draw a bar chart for the data: Monday 30 mm rain, Tuesday 10 mm, Wednesday 45 mm. Label axes.
- 中文: 根据以下数据绘制条形图：周一降雨量 30 mm，周二 10 mm，周三 45 mm。标注坐标轴。
12. Word Problems and Problem Solving | 应用题与问题解决
Every OCR paper includes multi‑step problems. The key is to read the question twice, underline numbers and keywords, and break the problem into smaller steps. Draw a diagram, bar model or number line when stuck. Always check if the answer makes sense in the context (e.g. a distance cannot be negative).
每份 OCR 试卷都包含多步应用题。关键在于读题两遍，划出数字和关键词，并将问题分解成更小的步骤。卡壳时，画图、条形模型或者数轴。始终检验答案在题境中是否合理（例如距离不能为负）。
- English: 'A pack of 6 pencils costs £1.50. How much for 8 packs? If you pay with a £20 note, what is your change?'
- 中文: “一包 6 支铅笔售价 £1.50。买 8 包需要多少钱？若你付一张 £20 的钞票，应找回多少？”
- English: 'The perimeter of a rectangle is 30 cm. Its length is twice the width. Find the dimensions.'
- 中文: “一个长方形的周长是 30 cm，长是宽的两倍。求长和宽。”
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